Previous studies have developed and tested methods to invert aspects of seismic data for elastic properties of Earth structure that are located either close to, or far from the seismic data receivers. When the data inverted are the actual seismic waveforms recorded, this process is called waveform inversion. These techniques compare seismic waveforms generated for a synthetic Earth model with those recorded; the model is then updated in such a way that the misfit between the two sets of waveforms is reduced. Hence, up to now waveform inversion studies have solved the wave equation in an Earth model to predict and then fit the particular waveforms that were recorded, where the predicted waveforms are derived from the wave equation solution. Such techniques include ground roll inversion and diving wave tomography. However, these techniques suffer from at least one of the following shortcomings: non-uniqueness of solution, sensitivity to noise, and unpractical source receiver configurations.